Removing ENSO-Related Variations from the Climate Record

GILBERT P. COMPO AND PRASHANT D. SARDESHMUKH

CIRES Climate Diagnostics Center, University of Colorado, and NOAA/Earth System Research Laboratory,

Physical Sciences Division, Boulder, Colorado

(Manuscript received 21 July 2008, in final form 16 November 2009)

ABSTRACT

An important question in assessing twentieth-century climate change is to what extent have ENSO-related

variations contributed to the observed trends. Isolating such contributions is challenging for several reasons,

including ambiguities arising from how ENSO itself is defined. In particular, defining ENSO in terms of

a single index and ENSO-related variations in terms of regressions on that index, as done in many previous

studies, can lead to wrong conclusions. This paper argues that ENSO is best viewed not as a number but as an

evolving dynamical process for this purpose. Specifically, ENSO is identified with the four dynamical ei-

genvectors of tropical SST evolution that are most important in the observed evolution of ENSO events. This

definition is used to isolate the ENSO-related component of global SST variations on a month-by-month basis

in the 136-yr (1871–2006) Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST). The

analysis shows that previously identified multidecadal variations in the Pacific, Indian, and Atlantic Oceans all

have substantial ENSO components. The long-term warming trends over these oceans are also found to have

appreciable ENSO components, in some instances up to 40% of the total trend. The ENSO-unrelated

component of 5-yr average SST variations, obtained by removing the ENSO-related component, is in-

terpreted as a combination of anthropogenic, naturally forced, and internally generated coherent multi-

decadal variations. The following two surprising aspects of these ENSO-unrelated variations are emphasized:

1) a strong cooling trend in the eastern equatorial Pacific Ocean and 2) a nearly zonally symmetric multi-

decadal tropical–extratropical seesaw that has amplified in recent decades. The latter has played a major role

in modulating SSTs over the Indian Ocean.

1. Introduction

Distinguishing anthropogenic from natural climate

variations is among the most important problems in

climate research today. Three kinds of natural variations

need to be considered. Variations of the first kind arise

from changes in external radiative forcing associated

with insolation changes and volcanic eruptions. Varia-

tions of the second kind are generated through internal

dynamical mechanisms of coherent long-term variabil-

ity in the ocean. Natural variations of the third kind,

that one may call climate noise, are associated with the

incoherent low-frequency imprint of phenomena with

shorter time scales. The dominant contributor to this noise

is the El Nino–Southern Oscillation (ENSO). ENSO is

the largest signal in the climate system on interannual

scales, but on longer scales it appears largely as noise.

Because its spectrum has a long low-frequency tail,

fluctuations in the timing, number, and amplitude of

individual El Nino and La Nina events within, say, 50-yr

intervals can give rise to substantial 50-yr trends. Such

trends are inherently unpredictable. Anthropogenic and

naturally forced climate changes, as well as coherent

(and therefore potentially predictable) internally gen-

erated long-term climate variations, have to be mea-

sured against this ENSO-related noise background to

appreciate their true significance around the globe.

Ideally, one would use ocean–atmosphere coupled cli-

mate models to estimate this background. Unfortunately,

many current models have substantial errors in repre-

senting tropical variability associated with ENSO (e.g.,

Newman et al. 2009; Zhang and McPhaden 2006; Joseph

and Nigam 2006). The dominant tropical empirical or-

thogonal function (EOF) pattern of sea surface temper-

ature (SST) variability in the models deviates substantially

from that in observations (Zhang and McPhaden 2006).

The models also do not reproduce the frequency power

Corresponding author address: Gilbert P. Compo, CIRES Cli-

mate Diagnostics Center and NOAA/ESRL/Physical Sciences

Division, 325 Broadway R/PSD1, Boulder, CO 80305-3328.

E-mail: compo@colorado.edu

VOLUME 23 J O U R N A L O F C L I M A T E 15 APRIL 2010

DOI: 10.1175/2009JCLI2735.1

� 2010 American Meteorological Society 1957

spectrum of the amplitude of the dominant observed

EOF pattern (Newman et al. 2009). This compromises

estimations of the ENSO-related component from model

simulations, leaving one to rely on some analysis of the

observed climate record itself for this purpose.

The problem of estimating and removing ENSO-

related variations from climate records has been ad-

dressed in many previous studies using a variety of

methods. Penland and Matrosova (2006, hereafter PM06)

discussed several difficulties with these methods. A com-

mon approach is to use a frequency bandpass filter

passing periods between approximately 2 and 6 years to

identify the ENSO-related variations (e.g., Parker et al.

2007; Folland et al. 1999; Lau and Weng 1999; Zhang

et al. 1997). This makes the strong assumption that all of

the SST variability in the chosen band, and none outside

it, is associated with ENSO. This is clearly un-

satisfactory, given the broadband nature of ENSO dy-

namics. It is not an accident that a substantial portion

of decadal and longer-term climate variability has been

found to be ENSO-like (e.g., Zhang et al. 1997; Alexander

et al. 2002; Newman et al. 2003; Schneider and Cornuelle

2005).

Another class of ENSO-removal methods involves

linear regression on the time series of some ENSO in-

dex, such as the Nino-3.4 SST index, the equatorial Pa-

cific cold tongue index, the Southern Oscillation index,

or the amplitude [i.e., principal component (PC)] of the

dominant EOF pattern of tropical SST variability (e.g.,

Robock and Mao 1995; Kelly and Jones 1996; Cane et al.

1997; Angell 2000; Chiang and Vimont 2004; Wheeler

and Hendon 2004; Thompson et al. 2008, 2009; Vyushin

and Kushner 2009). The index time series is sometimes

also bandpass filtered as an initial processing step. One

immediate difficulty with using such single-index defi-

nitions of ENSO is that no ENSO-unrelated variations

can occur in that index. If one uses the Nino-3.4 SST

index, for example, then no ENSO-unrelated ‘‘global

warming’’ signal can ever occur in the Nino-3.4 region—

by definition. This is also clearly unsatisfactory, given

climate model predictions of a significant change in this

region in the late twenty-first century in response to

greenhouse gas increases (e.g., Meehl et al. 2007).

There are other difficulties with following simple re-

gression approaches, as noted by PM06. One is that not

all ENSO-related variations occur in step around the

globe (Alexander et al. 2002 and references therein). For

example, ENSO-related SST anomalies in the tropical

Indian and Atlantic Oceans typically peak several months

after those in Nino-3.4 (e.g., Covey and Hastenrath 1978;

Lanzante 1996; Kumar and Hoerling 2003). Using time-

lagged regressions lessens the problem (Robock and

Mao 1995; Angell 2000; Vyushin and Kushner 2009) but

assumes that all frequency components are maximally

correlated at the same lag.

Regression onto the dominant SST PC time series is

additionally problematic: it assumes that ENSO is as-

sociated with the waxing and waning of a single SST

EOF pattern, which is inconsistent with observed ENSO

dynamics (e.g., Penland and Sardeshmukh 1995, here-

after PS95; Wallace et al. 1998; Vimont 2005). Some

investigators (e.g., Enfield and Mestas-Nunez 1999)

have addressed this limitation by regressing global SSTs

onto the complex PC time series of the dominant com-

plex EOF of global SSTs, which is associated with two

SST patterns. This is a step in the right direction, but it

ignores the fact that observed ENSO evolution involves

at least six patterns (PS95; Penland and Matrosova 1998;

PM06). A recent study by Guan and Nigam (2008) ad-

dressed this limitation by regressing global SSTs on the

PC time series obtained from a rotated extended EOF

(REEOF) analysis in which ENSO evolution was asso-

ciated with as many as 20 patterns.

Finally, an often overlooked aspect of almost all tra-

ditional ENSO-removal methods is the implicitly as-

sumed, but physically unjustified, orthogonality of the

ENSO-related and ENSO-unrelated variations. Con-

sider, for concreteness, the decomposition of the anom-

alous tropical SST state vector X(t) into its ENSO-related

and ENSO-unrelated parts as

X(t) 5 xe(t) 1 x

n(t) (1)

and a similar decomposition of the rest of the anomalous

climate state vector Y(t) as

Y(t) 5 ye(t) 1 y

n(t) ’ Ax

e(t) 1 y

n(t), (2)

in which, in the simplest approximation, one may as-

sume ye to be linearly related to xe (bold vectors through-

out the text refer to spatial patterns or fields). We stress

again that there is no physical basis for assuming the

orthogonality of xn and xe, or of yn and ye. However,

the common practice of using an A to estimate ye that is

based on linear regressions of Y(t) on xe(t) enforces an

orthogonality of yn and ye. Note also that yn and xn

need not be related (if they are related at all) through

the same A operator that links ye and xe. However,

even if they were so related and even if xn were or-

thogonal to xe, this would still not make yn orthogonal

to ye unless A were an orthogonal operator (i.e., ATA 5

cI), for which there is no physical justification. Similar

comments apply to methods determining yn(t) from

regressions of xn(t) onto Y(t) (e.g., Guan and Nigam

2008).

1958 J O U R N A L O F C L I M A T E VOLUME 23

PM06 proposed an alternative method for isolating xe,

based on the analysis of PS95, who had shown that the

evolution of tropical SST anomaly fields x(t) in a trun-

cated EOF space is well approximated over several

seasons by the linear equation x(t 1 t) 5 G(t)x(t) 1 e,

where G(t) 5 exp(Lt), L is a constant matrix, and e is

a noise vector. PS95 also showed that the development

of ENSO events is well approximated by the evolution

x(t) 5 G(t)x(0) from an ‘‘optimal’’ initial SST anomaly

field x(0) 5 f1 identified with the dominant right sin-

gular vector f1 of G (t 5 7 months). This evolution leads

to a mature ENSO pattern and subsequent decay, as

observed. PS95 stressed the pattern-changing aspect of

this evolution: f1 is distinct from the mature ENSO

pattern that it evolves into. Furthermore, this pattern-

changing evolution occurs almost entirely within a linear

vector space spanned by a three-mode subset fUkg of the

eigenmodes of L; that is, f1 is well approximated by

a linear combination of this subset. PM06 exploited this

fact to define the evolving ENSO-related part xe(t) of

tropical SST series x(t) as xe(t) 5 �ak(t)Uk.

Our principal goal in this paper is to isolate the

ENSO-related component of global SST variations on

a month-by-month basis in the 136-yr (1871–2006)

Hadley Centre Sea Ice and Sea Surface Temperature

(HadISST) data set (Rayner et al. 2003) using an ex-

tended form of PM06’s patterns-based filter. We define

the extratropical portions ye of the ENSO-related ex-

tratropical SST anomaly fields as those that are linked

to the tropical portions xe through the so-called ‘‘at-

mospheric bridge’’ (Alexander et al. 2002). This link is

established through relatively rapid extratropical atmo-

spheric responses to tropical SST changes and the sub-

sequent generation, by the associated altered surface heat

fluxes, of extratropical SST changes. We estimate the

effective ‘‘bridge’’ operator A empirically, from linear

regressions of extratropical SSTs onto tropical SSTs on

interannual time scales, and separately for each month

of the year (as explained later, this avoids the problem of

the false imposition of orthogonality between ye and yn

alluded to above). We then use this operator to estimate

the ENSO-related extratropical SST anomaly field ye

associated with the ENSO-related tropical field xe in

each month of the 136-yr dataset. Merging this extra-

tropical field with the tropical field yields the ENSO-

related global SST anomaly field in each month of the

dataset.

Removing the ENSO-related anomaly fields from the

full SST anomaly fields can substantially alter one’s

perception of multidecadal SST variability and long-

term SST trends around the globe, as will become evident

in the following sections. Figure 1 provides a preview. The

black curve shows the time series of globally averaged

10-yr running mean SST anomalies in the HadISST data-

set. The red curve shows the same series after its ENSO-

related components are removed. The modification is

appreciable, not just on decadal scales but even to the

long-term trend. The original series has an 1871–2006

trend of ;0.05 K decade21, consistent with Rayner

et al.’s (2003) estimate. After removal of the ENSO-

related components, that trend is reduced to ;0.03

K decade21.

Section 2 provides further justification and some im-

portant details of our method for isolating xe using a

dynamical ENSO patterns filter. Our preference for a

filter based on dynamical rather than statistical ENSO

patterns is partly motivated by evidence that the basic

dynamics of ENSO, as encapsulated in those eigen-

modes of L that are most important in the evolution of

ENSO events, have remained nearly constant over the

past 136 years, even if the statistics of ENSO have not.

Indeed a statistical-patterns-based filter requires an

even stronger assumption that the covariance structure

of the full tropical SST anomaly fields X(t), and not just

their ENSO-related parts xe(t), have remained constant

over the past 136 years, which is harder to justify in a

changing climate. Section 3 describes our procedure for

estimating the extratropical portions ye of the ENSO-

related SST anomaly fields. Section 4 presents some

surprising results obtained after removing the ENSO-

related anomaly fields from the full anomaly fields in

the HadISST dataset, including the effects on long-

term trends and on the dominant global patterns of low-

frequency (5-yr running mean) SST variations. Evidence

that the basic dynamics of ENSO have not changed

appreciably in the last 136 years is presented in section

5, and a discussion and concluding remarks follow in

section 6.

FIG. 1. Time series of the global ocean average surface temper-

ature anomaly (black curve) and its ENSO-unrelated component

determined using the ENSO patterns filter (red curve). A 10-yr

running mean has been applied to both series. Anomalies are rel-

ative to a 1949–2004 climatology.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1959

2. Tropical dynamical ENSO patterns filter

As mentioned above, the ENSO pattern filter (EPF)

developed by PM06 determines the ENSO-related portion

xe(t) of tropical SST anomaly fields as xe(t) 5 �ak(t)Uk,

where fUkg is a particular subset of the eigenmodes of

the matrix L in the linear model

dx(t)

dt5 Lx(t) 1 j(t), (3)

where j(t) is noise that is white in time but not neces-

sarily in space. The forward solution of (3),

x(t 1 t) 5 exp(Lt)x(t) 1 e 5 G(t)x(t) 1 e, (4)

describes tropical SST evolution over several seasons.

Here L is estimated using the observed lag-covariance

matrices C(t) 5 hx(t 1 t) x(t)Ti at two lags, t 5 0 and

t 5 to, as

L 51

to

lnfC(to)C(0)�1g, (5)

following the linear inverse modeling (LIM) procedure

described, for example, in Penland and Magorian (1993)

and PS95. Such a linear approximation can also be

consistently derived from forward dynamical models of

the coupled ocean–atmosphere system (PS95) and has

the advantage of correctly representing the observed

statistics, not only at the training lag to but at other lags

as well (PS95). That linear inverse models can capture

the dynamics of forward models was also shown more

generally by Garcia and Penland (1991), who showed

that a LIM could recover the linearized Navier–Stokes

equations from Monte Carlo simulations of explicitly

resolved gas particle interactions.

We applied the linear inverse modeling procedure to

the 1949–2004 HadISST data, taking care to cross-validate

the results (see appendix A). Maps of the cross-validated

local anomaly correlation skill for forecast lead times of

t 5 3, 6, 9, and 12 months show that (4) successfully cap-

tures the SST evolution in all tropical ocean basins at lead

times of up to a year (Fig. 2). Nearly identical skills were

obtained (not shown) with L operators estimated using

to 5 6 months and to 5 9 months in (5), further attesting

to the validity of (3) and (4).

As in PS95, we found that ENSO development is well

described by the evolution x(t) 5 G(t)x(0) from an

‘‘optimal’’ initial condition x(0) 5 f1 to a mature ENSO

condition x(8) 5 G(8)f1 5 g1c1 after 8 months, where

f1 and c1 are the normalized dominant right and left

singular vectors of G (8 months), respectively, and g1 is

the associated singular value. The spatial patterns of f1

and c1 are shown in Fig. 3. They strongly resemble those

obtained in previous studies using different datasets and

domains (PS95; Penland and Matrosova 1998; PM06;

FIG. 2. Maps of the local anomaly correlation between observed and predicted seasonal SST anomalies using the linear inverse model

prediction, Eq. (4). Maps are shown for forecast lead times of (a) 3 months, (b) 6 months, (c) 9 months, and (d) 12 months. Correlations are

computed over the period 1949–2004. The contour interval is 0.2, with a 0.95 contour added.

1960 J O U R N A L O F C L I M A T E VOLUME 23

Alexander et al. 2008). Figure 3c confirms that the pro-

jection of x(t) on f1 is a good predictor of Nino-3.4 SST

eight months later. The 8-month lead correlation of 0.65

is much higher than, for example, the 8-month lead cor-

relation of 20.2 obtained using the projection of x(t) on

the dominant SST EOF as the predictor.

The particular insight of PM06 was to use the de-

velopment from f1 as a basis for defining ENSO as

a stochastically perturbed evolving dynamical process.

Specifically, they defined the evolving ENSO-related

component xe(t) of the evolving tropical SST anomaly

fields x(t) as xe(t) 5 �ak(t)Uk, where fUkg is that subset

of the eigenvectors of L that contributes most to the

structure of f1. In other words, the ENSO-related evo-

lution is defined as the projection of Eq. (4) in this ei-

genvector subspace. Importantly, this does not require

ENSO events to develop precisely from f1 in all cases,

which of course they do not.

The evolution associated with each ENSO-relevant

eigenmode of L may be conveniently expressed and vi-

sualized in terms of the corresponding eigenmodes of

G(t) 5 exp(Lt). The eigenvectors of G(t) are identical

to the eigenvectors Uk of L, and the eigenvalues are

exp(bkt), where bk 5 sk 1 ivk are the corresponding

eigenvalues of L. Since G is real, its eigenvectors and

eigenvalues occur in complex conjugate pairs. These

pairs can be combined into a single real modal solution

xk(t) as

xk(t) 5 a

kcosv

kt 1 b

ksinv

kt

� �exp(s

kt), (6)

where ak and bk are real vectors with akTbk 5 0, ak

Tak 5 1,

and bkTbk $ 1 (see, e.g., Borges and Sardeshmukh 1995;

PS95). Without the exponential decay factor, the mode

traces out an ellipse in the space spanned by ak and bk

from the minor axis ak to the major axis bk, then to 2ak

and 2bk, and then back to ak. The e-folding decay time of

each mode is defined as 21/sk, its period as 2p/vk, and its

effective time scale as 1/jbkj. As the operator L is not self-

adjoint, its eigenvectors U are not orthogonal. Many

studies using both inverse and forward dynamical models

have found that the eigenvectors of the dynamical oper-

ator describing the evolution of the coupled tropical

ocean–atmosphere system are nonorthogonal (e.g., PS95;

FIG. 3. (a) The optimal initial SST anomaly structure that evolves into (b) the optimal ‘‘final’’ structure after eight

months. Each field is normalized to unity. Contour interval is 0.005. Shading is arbitrary and is the same sign in both

panels. (c) Time series of the projection of the optimal initial structure onto the observed SST anomalies (gray curve)

and Nino-3.4 time series shifted backward eight months (black curve). Both series have been normalized by their

respective standard deviations. The correlation between the gray and black series is 0.65.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1961

Penland and Matrosova 1998; Moore and Kleeman 1999;

Thompson and Battisti 2000; Alexander et al. 2008;

Newman et al. 2009). As such, nonorthogonality should

be an important feature of any pattern-based definition of

ENSO.

Following the objective procedure described in appen-

dix B yielded a subset of four ENSO-relevant eigen-

modes of our LIM. The least energetic spatial structure

a and most energetic spatial structure b associated with

each mode (6) are shown in Fig. 4, along with the ef-

fective time scale, period, and decay time. The associated

amplitude time series ak(t) (obtained by projecting

x(t) on the corresponding adjoint eigenvectors Vk) are

shown in Fig. 5. ENSO mode 1 corresponds very closely

to the PS95 ‘‘46 month’’ mode. The other modes are

difficult to compare directly with previous studies—

mainly because their real and imaginary parts were

shown at arbitrary phases in those studies, rather than

at their ‘‘least energetic’’ and ‘‘most energetic’’ phases

as in (6).

Our ENSO modes 1 and 2 are readily identifiable

with canonical ENSO evolution, each developing from

weak warm anomalies in the eastern equatorial Pacific

into strong warm anomalies there 4–12 months later.

Modes 1, 2, and 4 are associated with the previously

identified quasi-4-yr, 2-yr, and 5-yr to 6-yr periodicities

of ENSO (PS95; Moron et al. 1998). Modes 3 and 4 have

longer periods but relatively fast decay times, so one

does not expect to see more than about a quarter of the

implied oscillation in individual realizations. Even so,

these modes contribute to the overall evolution from

f1 to c1. Together with modes 1 and 2, they help to

explain the westward and eastward propagation of

ENSO events (PS95) and also ENSO events of differ-

ent ‘‘flavors’’ (e.g., Fu et al. 1986; Trenberth and Smith

2006).

Correlations among the modal amplitude time series

in Fig. 5 are listed in Table 1. While most of the ampli-

tude time series explain less than 1% of the variance of

other series, at least one phase of each mode has a sig-

nificant correlation with a phase of another mode. These

correlations reflect the nonorthogonality of these dy-

namically relevant structures.

Having determined the ENSO-relevant eigenmodes,

the ENSO-related parts xe(t) of the tropical SST anomaly

fields x(t) were determined as

FIG. 4. (left) Least energetic and (right) most energetic phases of the four dynamical ENSO modes used for defining the ENSO-related

tropical SST variations. The modes are ordered according to the projection of their adjoint onto the optimal initial structure shown in

Fig. 3a. Each mode’s effective time scale 1/jbj is indicated. Each mode evolves from (left) the least energetic phase a to (right) the most

energetic phase b, then to 2a, and then to 2b with the indicated period 2p/v while decaying with the indicated decay time scale 21/s. The

a phase is normalized to unity in the left panel. Note that the a and b phases of each mode are spatially orthogonal to each other by

construction.

1962 J O U R N A L O F C L I M A T E VOLUME 23

xe(t) 5 �

4

k51a

k(t)U

k5 �

4

k51[VT

k x(t)]Uk, (7)

and the ENSO-unrelated parts as the departures

xn(t) 5 X(t)� x

e(t) (8)

of the full (i.e., untruncated) SST anomaly fields X(t)

from xe(t). Note that, by construction, xe(t) in (7) pre-

serves the observed time evolution of the ENSO modes

and their constructive interference as observed during

the development of El Nino and La Nina events.

3. Extratropical ENSO-related variations

We define the ENSO-related parts ye(t) of the extra-

tropical SST anomaly fields Y(t) to be those that are

linearly linked to xe(t) as ye(t) 5 Axe(t), where A is

a linear atmospheric bridge operator. As stated earlier,

this atmospheric bridge is established through relatively

rapid extratropical atmospheric responses to tropical

SST changes and the subsequent generation, by their

associated altered surface heat fluxes, of extratropical

SST changes. We estimated A empirically, but bearing in

mind the discussion following Eq. (2), not by regressing

Y(t) on xe(t) but, instead, by regressing bandpass filtered

variations yb(t) of Y(t) in the 2–72-month period band

on similarly filtered simultaneous variations xb(t) of

X(t). We did this separately for 3-month seasons cen-

tered on each month of the annual cycle, obtaining and

using 12 distinct A matrices in all. Having determined

ye(t) using these A matrices, we then determined the

ENSO-unrelated parts yn(t) as yn(t) 5 Y(t) 2 ye(t).

The rationale for the above procedure was as follows.

First, since we define ye(t) to be the relatively fast extra-

tropical SST response to xe(t) through the atmospheric

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 a.

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 b.ENSO Mode 1: Effective timescale = 6.8 mo, Period = 49.1 mo, Decay Time = 14.0 mo

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 c.

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 d.ENSO Mode 2: Effective timescale = 3.4 mo, Period = 24.1 mo, Decay Time = 7.8 mo

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 e.

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 f.ENSO Mode 3: Effective timescale = 17.0 mo, Period = 434.1 mo, Decay Time = 17.5 mo

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 g.

1945 1960 1975 1990 2005

-3

-2

-1

0

1

2

3 h.ENSO Mode 4: Effective timescale = 3.9 mo, Period = 65.3 mo, Decay Time = 4.2 mo

Least Energetic Phase Most Energetic Phase

FIG. 5. Time series from 1949 to 2004 associated with the (left) least energetic and (right) most energetic phases of the four dynamical

ENSO modes from Fig. 4. Each mode’s effective time scale, period, and decay time are indicated. All series have been normalized to unit

standard deviation.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1963

bridge mechanism, we expect the matrix A linking them

to be the same as that linking all relatively fast extra-

tropical SST variations to all relatively fast tropical SST

variations. Hence our estimation of A through regressions

of yb(t) on xb(t). An important benefit of using such an A

is that we do not automatically impose a false orthogo-

nality between ye(t) and yn(t). Second, since A is essen-

tially a matrix of sensitivities of the fast extratropical SST

responses to tropical SST changes, then given that those

sensitivities vary from season to season (Newman and

Sardeshmukh 1998; Barsugli et al. 2006) it is desirable to

use a seasonally varying A for realistic estimations of ye.

To minimize edge effects when merging ye(t) with xe(t)

to construct the global ENSO-related SST anomaly fields,

we actually determined A as the appropriate submatrix of

a larger regression matrix ~A linking the global bandpass

filtered SSTs ~yb

to xb. We estimated this ~A separately for

each 3-month season in truncated spaces of the seasonally

dependent EOFs of xb and ~yb, retaining 20 and 15 EOFs,

respectively, of these fields in each season. The truncation

to 15 EOFs was chosen after an extensive cross-validation

exercise using the 1949–2004 data, withholding 8 years

of data per cross-validation set for all EOF truncations

between 2 and 28. The 15-EOF truncation yielded the

largest cross-validated hindcast skill of yb given xb,

in terms of both local anomaly correlation and rms

error averaged over all seasons and extratropical regions.

Figure 6 shows, for this optimal 15-EOF truncation, the

fractional variance of yb explained by xb, averaged over

all seasons. The tropical variations evidently account for

more than 10% of the extratropical variance almost ev-

erywhere and more than 50% of the variance over sub-

stantial areas.

To generate the global ENSO-related fields, we first

generated a preliminary set of global fields ~ye 5 ~Axe,

which were very close but not identical to xe in the

TABLE 1. Simultaneous cross-correlations of ENSO mode am-

plitude time series from 1949 to 2004 HadISST data. For each

mode, a is the least energetic phase and b is the most energetic

phase corresponding to Figs. 4 and 5. Assuming 3 degrees of free-

dom per year for seasonally averaged data, correlations of less than

0.16 are not statistically significant at the 5% level. Correlations in

bold are statistically significant above the 5% level. From the bi-

nomial theorem, six significant correlations are expected in 1.6% or

fewer sets of 28 tests.

Mode 1 Mode 2 Mode 3 Mode 4

a1 b1 a2 b2 a3 b3 a4 b4

Mode 1 a1 1 20.05 20.02 20.47 0.35 0.10 0.08 20.13

b1 1 0.07 0.06 20.04 20.02 0.03 0.21

Mode 2 a2 1 0.04 20.03 0.08 0.07 20.07

b2 1 20.11 20.07 0.02 20.02

Mode 3 a3 1 0.09 0.18 0.06

b3 1 0.34 20.09

Mode 4 a4 1 0.34b4 1

FIG. 6. Fraction of variance of bandpass filtered extratropical SST anomalies explained by similarly bandpass

filtered tropical SST anomalies using the atmospheric bridge operator A in the (a) Northern Hemisphere and

(b) Southern Hemisphere. All data were bandpass filtered using a Morlet wavelet filter with a response between 2 and

72 months. Contour interval is 0.2.

1964 J O U R N A L O F C L I M A T E VOLUME 23

tropics. We then created the final set ze(t) by merging ~ye

with xe as

ze(t) 5 (1� w)~y

e(t) 1 wx

e(t) (9)

using a cosine taper function w decreasing from a con-

stant value of 1 equatorward of 24.58 to zero poleward of

30.58. The global ENSO-unrelated variations were then

determined as departures of the full global SST anomaly

fields Z(t) from ze(t) as

zn(t) 5 Z(t)� z

e(t). (10)

The variance of seasonal zn(t) is shown in Fig. 7 at each

grid point as a fraction of the variance of seasonal Z(t).

The ENSO-unrelated SST variations account for more

than 10% of the variance of seasonal SST anomalies

throughout most of the tropics, a notable exception being

the region of large ENSO-related variability in the east-

ern Pacific. The ENSO-unrelated variations account for

more than 50% of the seasonal SST variance over large

portions of the extratropics during this period.

4. Results

We now present the results obtained after removing

the ENSO-related component from the full SST anom-

aly fields in the HadISST dataset, including the effects

on long-term trends and the dominant global patterns of

low-frequency (5-yr running mean) SST variations. We

also consider how removing the ENSO-related compo-

nent affects the time series of various low-frequency SST

indices, such as the Atlantic multidecadal oscillation

(AMO) index, associated with climate variability and

change.

a. Long-term SST trends

Figure 8a shows that almost all ocean basins have

warmed over the 1871–2006 period. This is in general

agreement with other estimates (e.g., Hansen et al. 2006).

The map shows that the warming has not been spatially

uniform. The warming trend pattern for a shorter period

of 1901–2005 is similar to that in Fig. 8a, but with some-

what larger amplitudes (see, e.g., Hegerl et al. 2007 and

appendix C). The ENSO-related contribution to the

1871–2006 trend, obtained using (9), is shown in Fig. 8b.

Not unexpectedly, it is largest in the eastern tropical

Pacific and negative in parts of the North and South Pa-

cific, consistent with the ‘‘low-frequency tail’’ of ENSO.

More surprisingly, it also accounts for an appreciable

fraction of the total warming trend in Fig. 8a in many

other regions.

The ENSO-unrelated part of the 1871–2006 trend,

obtained using (10), is shown in Fig. 8c. It accounts for

a large fraction of the total warming trend, especially

outside the tropics. The situation is much less clear in the

tropics, especially in the eastern tropical Pacific where

Fig. 8c shows a large ENSO-unrelated cooling trend.

This result is surprising, but broadly consistent with the

results of Cane et al. (1997) and Lau and Weng (1999)

obtained using different observational datasets and anal-

ysis techniques and those of Guan and Nigam (2008)

using the same HadISST dataset and the REEOF anal-

ysis technique.

Estimates of SST trends vary among reconstruction

datasets (Karnauskas et al. 2009; Vecchi and Soden 2007).

Nonetheless, appendix C shows that repeating our anal-

ysis using four different recent reconstructions yields

broadly similar ENSO-unrelated SST trends, including

a cooling trend in the eastern Pacific, despite differences

FIG. 7. Variance of ENSO-unrelated seasonal SST anomalies normalized by the total local seasonal SST anomaly

variance using HadISST data from 1949 to 2004. Contour interval is 0.2.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1965

in the details of the total SST trend. A cooling trend in the

eastern Pacific has been hypothesized to be a coupled

response to uniform radiative forcing (Clement et al.

1996; Cane et al. 1997). Notably, such a cooling response

is not produced in comprehensive coupled climate models,

although it has been found in ocean models subjected to

uniform radiative and enhanced absorbed shortwave

forcing (Seager and Murtugudde 1997; Sweeney et al.

2005).

As is well known, the global warming trend since the

late nineteenth century has not been constant but has

varied considerably on multidecadal time scales (e.g.,

Hegerl et al. 2007). It is therefore important to construct

versions of Fig. 8 for more recent periods in which the

warming appears to have accelerated. Figure 9 shows the

total, ENSO-related, and ENSO-unrelated SST trends

over the 1949–2006 period in the same format as Fig. 8 and

on the same scale. The generally larger trends in Fig. 9a

compared to Fig. 8a are consistent with previous esti-

mates using different datasets (e.g., Knutson et al. 2006).

Nonetheless, the same overall conclusions may be drawn

from Fig. 9 concerning the relative contributions of the

ENSO-related and ENSO-unrelated trends to the total

trend even over this shorter more recent period. This is

partly because the ENSO-related trend is also larger in

Fig. 9b than in Fig. 8b and remains generally reminiscent

of the low-frequency tail of ENSO.

The ENSO-unrelated part of the 1949–2006 trend is

shown in Fig. 9c. Its generally similar pattern, but weaker

amplitude, compared to the observed trend in Fig. 9a

suggests that it accounts for approximately two-thirds

of the observed trend in most regions. The interesting

ENSO-unrelated cooling trend in the eastern equatorial

Pacific now appears with even larger amplitude than in

Fig. 8c but is more meridionally confined. It is tempting

to speculate that such a cooling is dynamically consistent

with an enhancement of surface easterlies and equato-

rial upwelling over the eastern Pacific in response to the

strong ENSO-unrelated recent warming of the Indian

and west Pacific Oceans.

b. Dominant patterns of low-frequencySST variations

Linear trend maps such as Figs. 8 and 9 fail to capture

the detailed structures of observed multidecadal and

longer-term variations (e.g., Parker et al. 2007 and ref-

erences therein). An EOF analysis can be more re-

vealing in this regard. The left panels of Fig. 10 show the

FIG. 8. Global maps of linear trends over 1871–2006 of (a) the full

HadISST SST anomalies, (b) the ENSO-related anomalies, and (c)

the ENSO-unrelated anomalies. Contour interval is 0.28C change

per 50 years. The zero contour is thickened.

FIG. 9. As in Fig. 8 but for trends over 1949–2006.

1966 J O U R N A L O F C L I M A T E VOLUME 23

two leading EOFs and associated PCs of 5-yr running

mean HadISST anomalies in the 1871–2006 period. The

first EOF of such long-term SST variations is often

identified with global warming (Parker et al. 2007). Note

that it is similar, but not identical, to the long-term trend

pattern in Fig. 8a. The second EOF is often identified

with ENSO-like decadal variability (Zhang et al. 1997),

a global signature of the Pacific decadal oscillation or the

interdecadal Pacific oscillation (Parker et al. 2007). It is

strongly reminiscent of the low-frequency tail of ENSO

and has, indeed, been argued to be such in previous

studies (e.g., Alexander et al. 2002; Newman et al. 2003;

Schneider and Cornuelle 2005; Alexander et al. 2008).

The two leading EOFs and associated PCs of the

ENSO-unrelated 5-yr running mean SST variations are

shown in the right panels of Fig. 10, in the same format as

the left panels. The first EOF of these ENSO-unrelated

variations is generally very similar to the first EOF of

the total variations in Fig. 10a, but not in the tropics. In

particular, the eastern Pacific cooling emerges as an

important part of this leading pattern, of which there is

only a hint in Fig. 10a.

The second EOF of the ENSO-unrelated variations,

shown in Fig. 10d, is strongly suggestive of a nearly zonally

symmetric multidecadal tropical–extratropical seesaw

(TESS). A very similar pattern was identified by Livezey

and Smith (1999) as importantly related to North Amer-

ican climate variations, but was interpreted by them as a

‘‘global climate change signal’’ associated with anthro-

pogenic warming. Although the PC time series in Fig. 8d

does show a strong ‘‘trend’’ from the 1950s to the 1990s,

the multidecadal oscillatory nature of the variation is

more obvious in the full record. The tropical aspect of

this variation was also identified and interpreted as a

tropical ‘‘trend’’ pattern by PM06, but again using a

shorter record. As in that study, the PC time series in

Fig. 10d has a parabolic shape from the 1950s to the

present; however, there is no trend over the full record.

These variations appear to be related to the global cir-

culation and precipitation changes, claimed by Baines and

Folland (2007) to be associated with an ‘‘abrupt climate

shift’’ in the late 1960s, and to changes in Sahel rainfall

(see also PM06). A relatively sudden upturn in the late

1960s is also evident in our PC time series in Fig. 10d.

FIG. 10. (left) The two leading EOFs and associated PCs (inset) of 5-yr running mean SST anomalies from the 1871–2006 HadISST

dataset and (right) the same quantities computed using the ENSO-unrelated SST anomalies. The fraction of variance explained in (a),(c)

the original dataset and (b),(d) the ENSO-unrelated dataset is indicated over each panel. Note that the PCs are normalized to have unit

amplitude, while the EOFs show the observed magnitude (8C) for a unit deviation of the PC. The contour interval is 0.058C.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1967

Overall, Fig. 10 shows that one can get quite a differ-

ent impression of low-frequency SST variations around

the globe in the last 136 years after their ENSO-related

components are removed. We interpret the ENSO-

unrelated variations as representing a combination of

anthropogenic, naturally forced, and internally gener-

ated coherent multidecadal variations. It is far beyond

the scope of this study to attempt a further split into

these three component variations. Still, it is tempting to

associate EOF-1 of the ENSO-unrelated variability with

‘‘forced’’ and EOF-2 with ‘‘natural internal’’ variability,

mainly because PC-1 has a strong long-term trend and

PC-2 has no trend. If EOF-2 is, indeed, indicative of a

natural multidecadal tropical–extratropical seesaw, then

its general upward trend from the 1950s to the 1990s

may have been misinterpreted in the climate commu-

nity as an accelerated ‘‘forced’’ trend and its sharp

upturn in the 1960s as an anthropogenic abrupt climate

shift. Its relatively large amplitude over the Indian

Ocean (compared to EOF-1) suggests that it has played

a major role in modulating Indian Ocean SSTs over the

last half century, which have also been implicated in

several climate change attribution studies (e.g., Hurrell

et al. 2004).

c. SST-based climate indices

SSTs averaged over various large representative areas

are widely used as indices of climate variability. The

global ocean SST average is one such commonly used

measure (Hegerl et al. 2007). As already shown in Fig. 1,

removing its ENSO-related component reduces its 136-yr

warming trend by 40% from ;0.05 to ;0.03 K decade21.

This is also consistent with Angell’s (2000) analysis of

tropospheric air temperatures, who found that about

two-thirds of the overall trend in his data was ENSO

unrelated.

The effect of removing ENSO-related components

from two other climate indices is illustrated in Fig. 11. The

west Pacific/Indian Ocean warm pool encompasses the

area of warmest SSTs on the planet. Global mean surface

temperature and precipitation are particularly sensitive

to SST changes in this area (Barsugli et al. 2006). The

black curve in Fig. 11a shows the 10-yr running mean time

series of SSTs averaged over the warm pool. Removing

its ENSO-related component yields the ENSO-unrelated

red curve. It is remarkable that the ENSO-unrelated time

series shows a slight cooling trend from ;1900 to the mid-

1970s, followed by an abrupt warming and stabilization.

The ENSO-related variations have clearly contributed

substantially to the observed full time series, contributing

a warming influence in the early twentieth century, a

cooling influence in the 1980s, and again a warming in-

fluence in the early twenty-first century.

Another climate index that has received consider-

able attention is the index of the Atlantic multidecadal

oscillation (AMO) (e.g., Enfield and Mestas-Nunez 1999;

Delworth and Mann 2000), especially for its purported

links to Atlantic hurricane variability (Goldenberg et al.

2001), global drought (McCabe and Palecki 2006), and

European climate (Parker et al. 2007). It has been sug-

gested that this oscillation may be natural and predictable

(Knight et al. 2005). Here we define the AMO index,

following Enfield et al. (2001), as the linearly detrended

area-averaged North Atlantic SST. Its 10-yr running

mean time series is shown as the black curve in Fig. 11b.

The multidecadal variations discussed in numerous pre-

vious studies are evident and consistent with other data-

sets and AMO definitions [see Delworth and Mann

(2000)]. The version of the AMO index with its ENSO-

related components removed is shown as the red curve. It

is not aligned precisely with the full index series after

about 1990, but is extremely close; to that extent, it con-

firms that much of the recent increase in detrended North

Atlantic SSTs is only weakly ENSO related. In other

periods, however, the discrepancy between the black

and red curves is indicative of a considerable ENSO

influence, such as contributing to an enhancement of the

oscillation from ;1900 to the 1950s. Insofar as such ENSO

contributions are climate noise, these results suggest

that modeling studies of North Atlantic climate variations

(e.g., Delworth and Mann 2000; Knight et al. 2005) may

have greater success comparing their simulated variations

with the ENSO-unrelated variations shown here than

with the full observed variations.

5. Constancy of ENSO dynamics

The overarching conclusion of this study is that both

long-term trends and multidecadal variations over the

last 136 years in the Pacific, Indian, and Atlantic Oceans

have had substantial ENSO-related components. Be-

cause our estimates of these components are somewhat

larger than reported in previous studies, and to that

extent are also somewhat surprising, it is necessary to

reassess some of the assumptions of our analysis. One

particular assumption, which we maintain is much weaker

than made in other ENSO-removal studies but is never-

theless still an assumption, is that the dynamics of ENSO

have remained roughly constant over the last 136 years,

even if their statistics have not. By this we mean that the

ENSO-relevant eigenmode subset of the tropical dy-

namical evolution operator L, shown in Fig. 4, has re-

mained roughly the same in the last 136 years. In the

following, we pursue two different lines of evidence in

support of this claim; specifically that L itself has not

shown a systematic trend over the last 136 years.

1968 J O U R N A L O F C L I M A T E VOLUME 23

It has long been thought that one of the most impor-

tant controlling influences on ENSO dynamics is DTE–W,

the east–west SST gradient across the tropical Pacific

basin (Bjerknes 1969; Neelin et al. 1998 and refer-

ences therein; Sun 2003). Figure 12 shows that, although

DTE–W has varied throughout the record, with 10-yr av-

eraged values of up to 25% larger or smaller than the

1871–2006 average, it has not shown a systematic trend

over the entire record. To be sure, there is evidence of an

upward ‘‘trend’’ after 1900 (Cane et al. 1997) and in the

most recent 50 years (Zhang and McPhaden 2006), but it

is clear that they are part of long-term variability with no

obvious overall trend.

If the relatively modest long-term variations in DTE–W

were important in modulating ENSO variability, one

might expect such a modulation to be evident in the

variance of ENSO indices such as Nino-3.4 SSTs. The

gray shaded curve in Fig. 12 shows the time series of

2–6-yr variance in Nino-3.4 from the HadISST dataset,

produced following the method of Torrence and Compo

(1998). While there are hints of an association, say during

the 1890s and in the most recent decades, there are also

periods of large Nino-3.4 variance coexisting with those

of weak gradients, such as the early 1900s. These vari-

ations of Nino-3.4 variability are consistent with those of

other ENSO indices such as Nino-3, the Southern Os-

cillation index (SOI) (Torrence and Webster 1999), and

central Pacific rainfall (Kestin et al. 1998).

It has recently been suggested that the interaction of

the subtropical ocean with the equatorial ocean through

FIG. 11. SST time series of the (a) warm pool and (b) Atlantic multidecadal oscillation (black

curves) and their ENSO-unrelated components (red curves). A 10-yr running mean has been

applied to all series. Anomalies are relative to the 1949–2004 climatology. Area averages are

computed over the regions indicated on the respective inset maps: (a) warm pool (158N–158S,

608–1658E) and (b) AMO (908N–08, 808W–08).

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1969

‘‘oceanic tunnels’’ may also be important in modulating

ENSO dynamics (e.g., Seager and Murtugudde 1997;

Kleeman et al. 1999; Shin and Liu 2000; Sun et al. 2004;

Solomon et al. 2008). A simple proxy for this effect is

the SST gradient between the north subtropical and

tropical Pacific SSTs DTN–S. The blue curve in Fig. 12

shows that decadal variations in this gradient have been

less than 20% of the long-term mean. Again, there is no

obvious correspondence with changes of Nino-3.4 SST

variance. Although large changes of DTN–S could be

expected to impact ENSO (Collins 2000; Sun et al.

2004), the observed changes have apparently not been

large enough in this regard. As such, they have probably

not altered the tropical dynamics represented in L. They

do not appear to be related consistently to variations in

the statistics of Nino-3.4 SSTs or to those of other ENSO

indices (Wang and Wang 1996; Torrence and Compo

1998; Kestin et al. 1998; Torrence and Webster 1999).

Another way of assessing the near constancy of L is to

ask to what extent does the forecast skill of the model (4)

vary over the 136 years of record if one uses a constant L

to make the forecasts. Figure 13 shows the 136-yr time

series of the pattern correlation of the observed and

predicted seasonal tropical SST anomaly fields for var-

ious forecast lead times. Recall that the model (i.e., the L

operator) was developed using the 1949–2004 data at

a 3-month lag. Therefore all comparisons for 1871–2006

at 6-month and 12-month lags are independent tests, as

is the forecast skill for 1871–1948 at the 3-month lag. The

relative constancy of the forecast skill is remarkable.

The drop in skill between the 1910s and 1950s may re-

flect reduced observation availability during the world

wars but may also be associated with decreased ENSO

variability itself in the period, as reflected in several

ENSO indices (Wang and Wang 1996; Torrence and

Compo 1998; Kestin et al. 1998; Torrence and Webster

1999) and illustrated for Nino-3.4 SSTs in Fig. 12.

Taken together, the evidence in Figs. 12 and 13 sug-

gests that the tropical ocean dynamics encapsulated in L

have not changed appreciably in the last 136 years. A

similar conclusion was reached by Chen et al. (2004) for

the last 150 years using a forward coupled model of in-

termediate complexity. It is of course true that for suffi-

ciently large changes in the basic state, such as represented

in DTE–W or DTN–S, one would expect L to be sufficiently

altered to reduce the advantages of our ENSO-removal

method over other methods. So far, however, the basic-

state changes appear to have been small enough to justify

our linear decomposition throughout the 136-yr period

of record.

FIG. 12. (top) Time series of east–west and north–south Pacific SST differences scaled by

their respective long-term mean values. Black curve: temperature difference between Nino-3.4

and western Pacific warm pool DTE–W. The mean difference over 1871–2006 is 21.988C. Blue

curve: temperature difference between the north subtropical and tropical Pacific DTN–S. The

mean difference over 1871–2006 is 21.748C. A 10-yr running average has been applied to the

difference series. Regions are shown on the inset map. Black boxes: DTE–W (58N–58S, 1708–

1208W) minus (58N–58S, 1208–1708E); blue boxes: DTN–S (158N–258N, 1208E–908W) minus

(108N–108S, 1208E–908W). (bottom) Gray shaded curve: variance of Nino-3.4 SST anomalies in

the 2- to 6-yr band determined from wavelet analysis.

1970 J O U R N A L O F C L I M A T E VOLUME 23

Given the evidence of the near constancy of L, one

might wonder if we could have used the entire 136-yr

record to construct L. We found that we could not have,

owing to sparse observations in key regions in the early

part of the record. For example, we estimated L using

the 1872–1947 data. The optimal final structure c1

using these data had a pattern correlation with the c1

in Fig. 3b of 0.95. However, f1, the optimal initial

structure, had a pattern correlation with the f1 in Fig. 3a

of only 0.25. One could have anticipated this result

after considering the data availability in regions in

which these structures have large amplitude (Fig. 14).

Figure 14a shows the number of SST observations in

the International Comprehensive Ocean–Atmosphere

Data Set (ICOADS) collection (Worley et al. 2005),

which represents a superset of that used to construct

the HadISST fields, in March through May in two re-

gions where f1 has large amplitude. The data avail-

ability in March–May is relevant since this is when

most ENSO events emerge (PS95; Harrison and Larkin

1998). There were clearly far fewer observations in

these months in these key regions in the late nineteenth

and early twentieth centuries. In contrast, the central

equatorial Pacific region of large amplitude of c1

was well observed in the mature December–February

phase of ENSO throughout the record (Fig. 14b). It was

in recognition of such constraints on data availability

that we decided to estimate L using the more recent

1949–2004 period in which there were sufficient ob-

servations to determine both f1 and c1 with sufficient

accuracy.

6. Summary and conclusions

In this paper, we have argued that identifying and

removing ENSO-related variations by performing re-

gressions on any single ENSO index can be problematic.

We stressed that ENSO is best viewed not as a number

but as an evolving dynamical process for this purpose.

Specifically, we identified ENSO with those four dy-

namical eigenvectors of tropical SST evolution that are

most important in the observed evolution of ENSO

events over several seasons. We used this definition to

isolate the ENSO-related component of global SST var-

iations on a month-by-month basis in the 136-yr (1871–

2006) HadISST dataset.

We find that removing ENSO-related variations has a

large effect on long-term SST trends and on the domi-

nant patterns of low-frequency (5-yr running mean)

SST variability. We interpret the low-frequency ENSO-

unrelated SST variations as reflecting an as yet undeter-

mined combination of anthropogenic, naturally forced,

and coherent internal multidecadal variations. The first

EOF of the ENSO-unrelated data has a general global

warming structure, but also a pronounced cooling in the

eastern equatorial Pacific, which, although surprising, is

not unphysical. The second EOF is strongly suggestive of

a multidecadal zonally symmetric tropical–extratropical

SST seesaw pattern. It is not clear to what extent it re-

flects a pattern of forced or natural variability. We are

more inclined toward interpreting it as the latter, given

that the amplitude time series of this pattern has no

trend over the last 136 years.

FIG. 13. Time series of the pattern correlation between forecast and observed tropical SST

anomaly fields from 1871 to 2006. Forecast skill is shown for leads of 3 months (red curve),

6 months (blue curve), and 12 months (pink curve). A 10-yr running mean has been applied.

Gray shading indicates the 95% range of expected fluctuations about the 1949–2004 mean value

at each lag.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1971

It is important to recognize that our decomposition

of the low-frequency SST fields into ENSO-unrelated

and ENSO-related parts is not strictly the same as into

‘‘predictable’’ and ‘‘unpredictable’’ parts. The ENSO-

unrelated parts may be predictable if the relevant an-

thropogenic and natural radiative forcings are predictable

and the appropriate initial conditions for coherent inter-

nal long-term variations are known. The ENSO-related

parts, as identified by us, include both the unpredictable

low-frequency tail of ENSO and the potentially predict-

able projection of anthropogenic and naturally forced SST

variations on the eight ENSO mode patterns in Fig. 4. In

other words, our ENSO-unrelated low-frequency fields

may be mostly predictable, but our ENSO-related fields

may not be totally unpredictable. (Nonetheless, we sus-

pect that any such ENSO-related low-frequency pre-

dictability was small in our period of interest, as there is

no obvious trend in any of the ENSO modal time series

in Fig. 5 that one could immediately attribute to an an-

thropogenically forced or naturally forced response.) This

comment applies equally, of course, to any other pattern-

based method, including all EOF-based methods, of

identifying ENSO-related climate variations.

These issues are schematically illustrated in Fig. 15.

Each circular ring, representing the totality of any par-

ticular climate variation (e.g., a 50-yr trend field), is

divided into two segments depending on the type of de-

composition employed. Three types of decompositions

are considered. With regard to a 50-yr trend field, for

instance, they would represent decompositions of the

field into anthropogenic and natural, predictable and

unpredictable, and ENSO-unrelated and ENSO-related

components. The important point illustrated in Fig. 15 is

that, although it is tempting to think so, such decom-

positions are in general not strictly congruent. In other

words, anthropogenic 6¼ predictable 6¼ENSO unrelated,

and natural 6¼ unpredictable 6¼ ENSO related, in the

strictest sense. (For example, if an anthropogenic climate

trend pattern has a large projection in the space of the

ENSO modes shown in Fig. 4, then that projected trend

component will also contribute to the ENSO-related

trend obtained by our method. The nearly zero long-

term trend in the time series of the ENSO modes shown

in Fig. 5 suggests, however, that such contributions were

small over the twentieth century.) This noncongruence

is indicated in Fig. 15 by the overlap at the segment

FIG. 14. Time series of the number of SST observations available in the ICOADS collection for selected seasons

and regions from 1871 to 2006. (a) During March through May in two regions of large loading of the optimal initial

structure [see inset (108–38N, 1408E–1658W); (228–308S, 1608–1058W)]. (b) During December through February in the

region of large loading of the optimal evolved structure [see inset (68N–78S, 858W–1808)]. The number of observa-

tions is shown on a logarithmic scale. The thin line in both panels indicates 500 SST observations per season.

1972 J O U R N A L O F C L I M A T E VOLUME 23

boundaries. Such overlaps complicate climate diagnosis,

but they are real and arise from the physically based

nonorthogonality of the component variations in both

the spatial and temporal domains. Assuming orthogo-

nality in either of these domains for diagnostic expe-

diency can lead to wrong conclusions. An example of

spatial nonorthogonality, with regard to ENSO, is that

the anthropogenic signal in global temperature is not

spatially orthogonal to the global ENSO signal; after all,

1998 remains the warmest year of the instrumental re-

cord since 1850, according to Brohan et al. (2006). As is

already well accepted, ENSO plays a role in global mean

temperature variations (e.g., Robock and Mao 1995;

Kelly and Jones 1996; Angell 2000; Thompson et al.

2008, 2009). Therefore, any definition of ENSO must

account for the global mean part of the phenomenon.

An example of temporal nonorthogonality, again with

regard to ENSO, is that ENSO is not a frequency-band-

limited phenomenon and clearly has a low-frequency

tail, so any definition of ENSO must account for that

low-frequency tail, as stressed repeatedly in this paper.

Our demonstration that ENSO-related trend compo-

nents account for a substantial part of twentieth-century

SST trends provides strong motivation for accurately

representing the ENSO eigenmodes documented here in

climate models, regardless of the relative magnitudes of

the unpredictable noise and potentially predictable an-

thropogenic contributions to those ENSO-related trends.

This is because, on the one hand, the very existence

of unpredictable trend components associated with the

low-frequency tail of ENSO necessitates an accurate

representation of ENSO dynamics and ENSO-related

climate variability that, even if it is just noise, can strongly

affect multidecadal and longer-term climate variations

around the globe. On the other hand, a substantial future

anthropogenic forcing of the ENSO eigenmodes would

affect not only ENSO dynamics but also the spatial pat-

tern of the tropical SST change, with important implica-

tions for global climate change (Barsugli et al. 2006).

Acknowledgments. We thank colleagues in the Climate

Diagnostics Center of CIRES/CU and in NOAA/ESRL/

PSD, especially C. Penland, A. Solomon, M. Newman,

and M. Alexander for useful discussions and C. Smith

for help with the SST data. We thank C. Folland of UKMO

for discussions regarding the AMO and M. Wallace of

the University of Washington for discussions regarding al-

ternative ENSO-removal procedures. For providing their

SST data, we thank the Hadley Centre, N. Rayner, and

BADC for HadISST, NOAA/NCDC and T. Smith for

ERSST, the IRI and A. Kaplan for LDEO, and the JMA

and M. Ishii for COBE. We appreciate stimulating com-

ments made by three anonymous reviewers on an earlier

version of the manuscript. This work was supported by the

NOAA Climate Program Office.

APPENDIX A

Details of Linear Inverse Model implementation

As discussed in PS95, a consistency requirement for

the validity of (3) and (4) is that the estimate of L be

FIG. 15. (left) Circular rings schematically illustrate the totality of any particular climate

variation (e.g., a 50-yr trend). Each ring is divided into two segments depending on the de-

composition used. Two types of decompositions are predictable and unpredictable (outer red

and blue ring) and anthropogenic and natural (inner red and blue ring). The gray arcs over-

lapping the segment boundaries illustrate that these decompositions are not necessarily con-

gruent; e.g., some natural climate variations may be predictable. (right) The relationships

between a third, ENSO/non-ENSO decomposition (solid black and perforated ring) and the

other two decompositions are illustrated. For clarity, the labels are not repeated from the left

panel. The three rings illustrate how, e.g., the non-ENSO component may be generally iden-

tified with the anthropogenic and predictable components of climate variations but with the

gray arcs again emphasizing that the congruence is not exact.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1973

independent of the particular choice of to. In this study,

we used to 5 3 months as in PM06 and the 1949–2004

monthly HadISST SST data to estimate the C(0) and

C(to) matrices. The choice of the second half of the

HadISST dataset for this purpose was partly motivated

by the fact that 1949 marks a significant increase in the

input data density used in constructing the dataset

(Rayner et al. 2003) and partly by a need to leave an

‘‘independent’’ first half for assessing the dynamical

stationarity of L. As in PM06, L was estimated using

SSTs in the entire tropical domain 308N–308S. Penland

and Matrosova (1998) show that the LIM results ob-

tained using this domain are similar to those obtained

using a more limited Indo-Pacific domain. Three-month

running mean anomalies were formed at each grid point

as differences from the 1949–2004 monthly average an-

nual cycle. The 18 data were spatially smoothed using a

38 latitude, 58 longitude boxcar smoother. These smoothed

fields were then projected on a truncated space of 20 SST

EOF patterns, retaining about 89% of the SST variance.

The time varying coefficients of these 20 EOFs, that is,

the 20 PC time series, define the truncated 20-component

tropical SST vector x(t) used for isolating xe(t) in this

study.

Extensive sensitivity and cross-validation exercises

were performed for all EOF truncations from 2 to 30

before settling on the choice of 20 EOFs, using the skill

of tropical SST hindcasts based on (4) as a guiding cri-

terion. This was done by excluding, in turn, each of eight

contiguous 7-yr segments from the data, estimating L

from the remaining 49 years, and then performing hind-

casts in the excluded 7-yr segment. The best average

hindcast skill was obtained for a 20-EOF truncation, in

terms of both anomaly pattern correlation skill and rms

error over the domain.

APPENDIX B

Objective Selection of ENSO-Related Eigenmodes

We determined the ENSO-relevant subset fUkg of the

eigenvectors of L objectively as follows. First, we imposed

a time-scale constraint consistent with the 18–24-month

upper bound on ENSO predictability found in previous

studies (e.g., PS95; Chen et al. 2004). Modes with a decay

time scale of longer than 24 months cannot contribute

to predictable ENSO evolution, otherwise ENSO pre-

dictability would extend beyond 24 months. We there-

fore excluded modes with a longer decay time scale.

Using the shorter 18-month limit of PS95 did not affect

the result since this criterion excludes only one eigen-

mode of L, a purely decaying mode with a decay time

scale of ;40 months. A similar mode was also excluded

by PM06. The remaining modes were ranked by the

magnitude of the inner product of their corresponding

adjoint eigenvector Vk (i.e., the eigenvector of LT with

the same eigenvalue) with f1. Then, starting with the

mode having the largest inner product and longest effec-

tive time scale, a truncated G (8) operator was constructed

FIG. C1. Global maps of linear trends over 1901–2005 from four different SST datasets: (a) HadISST v1.1, (b) NOAA ERSST version 3,

(c) LDEO SST version 2, and (d) COBE SST. Contour interval is 0.28C change per 50 years. The zero contour is thickened.

1974 J O U R N A L O F C L I M A T E VOLUME 23

using only this eigenmode. Its dominant right and left

singular vectors and singular value were compared with

the f1, c1, and g1 obtained from the full G (8) operator.

If the pattern correlations exceeded 0.5, the mode was

included in the ENSO-relevant subset; if not, the pro-

cedure was repeated for succeeding modes in the ranked

list until they did. The criterion for including additional

modes in the subset was whether their inclusion improved

the approximation to f1, c1, and g1. A mode was included

if the pattern correlations with f1 and c1 increased, and

the singular value also increased, or decreased by less than

5% of g1. Applying this procedure yielded a total of four

ENSO-relevant eigenmodes (Fig. 4). Remarkably, we

found this selection algorithm to be completely in-

sensitive to the order of consideration of the subsequent

modes when the threshold pattern correlation for se-

lection of the first member of the subset was set at 0.5 or

higher.

APPENDIX C

Comparison of SST Trends Using Different SSTDatasets

Global SST trends for 1901–2005 computed using four

different datasets are shown in Fig. C1. The period was

chosen to facilitate comparison with similar trends con-

tained in the Intergovernmental Panel on Climate Change

(IPCC) Fourth Assessment report (Hegerl et al. 2007;

Trenberth et al. 2007). Least squares linear trends were

computed using the HadISST1.1 dataset, National Oce-

anic and Atmospheric Administration (NOAA) Extended

Reconstructed SST (ERSSTv3) (Smith et al. 2008),

Lamont Doherty Earth Observatory SST (LDEOv2)

(Kaplan et al. 1998), and Centennial in Situ Observa-

tion Based Estimates of SST (COBE) (Ishii et al. 2005).

The datasets differ in their input SST observations and

methods of interpolation. Unlike the HadISST, ERSST,

and LDEO datasets, the COBE optimal interpolation

dataset does not employ an EOF basis (Ishii et al. 2005;

M. Ishii 2009, personal communication). Instead, COBE

uses a variational scheme with prespecified optimal anal-

ysis parameters. Comparing the four datasets, we see that

the trends are generally similar (Table C1), with ap-

parent discrepancies in the equatorial Pacific (see also

Vecchi and Soden 2007), western Indian Ocean, North

Pacific, and south of Greenland (Fig. C1). The two data-

sets that make no assumption about the spatiotempo-

ral structure of low-frequency variability (LDEO and

TABLE C1. Pattern correlations between four observational SST

datasets of 1901–2005 SST trend from 608N to 608S with (and also

without) the area mean included.

HadISST

NOAA

ERSSTv3 LDEO COBE

HadISST 1 0.91 (0.59) 0.89 (0.63) 0.91 (0.64)

NOAA

ERSSTv3

1 0.89 (0.53) 0.93 (0.54)

LDEO 1 0.89 (0.57)

COBE 1

FIG. C2. As in Fig. C1 but for ENSO-unrelated trends.

15 APRIL 2010 C O M P O A N D S A R D E S H M U K H 1975

COBE, Figs. C1c and C1d) appear to agree more closely

with the spatial variations of the HadISST trend map

than does the NOAA ERSSTv3b (Table C1), particu-

larly in the eastern equatorial Pacific trend representing

a relative minimum compared to the rest of the tropics.

A comprehensive comparison of these datasets, including

their trends and variability, is beyond the scope of the

present study. Other researchers (M. Newman 2009,

personal communication) and the Global Climate Observ-

ing System Working Group on Sea Surface Temperature

and Sea Ice (T. Brandon 2009, personal communication)

are undertaking such an investigation.

Our EPF from Eq. (10) has been applied to all four

datasets to form an estimate of the ENSO-unrelated

trend (Fig. C2). It is remarkable that, despite the use of

a different ENSO-removal technique and 15 additional

years of data, we obtain nearly the same ENSO-unrelated

trend as found by Cane et al. (1997), as evident from a

comparison of Fig. C2c with their Fig. 3b (not shown

here). In general, the ENSO-unrelated trend patterns

from all four datasets are broadly similar (Table C2).

In particular, all four show that the long-term ENSO-

unrelated trend in the eastern equatorial Pacific is one of

cooling. This regional cooling trend is also evident in

trends over other periods (as in Figs. 8 and 9) and in

previous studies (Cane et al. 1997; Lau and Weng 1999;

Guan and Nigam 2008).

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